quacau {lmomco} | R Documentation

## Quantile Function of the Cauchy Distribution

### Description

This function computes the quantiles of the Cauchy distribution given parameters (xi and α) of the distribution provided by `vec2par`. The quantile function of the distribution is

x(F) = xi + α times tan(π(F-0.5)) mbox{,}

where x(F) is the quantile for nonexceedance probability F, xi is a location parameter and α is a scale parameter. R supports the quantile function of the Cauchy distribution through `qcauchy`. This function does not use `qcauchy` because `qcauchy` does not return `Inf` for F = 1 although it returns `-Inf` for F = 0.

### Usage

    quacau(f, para)

### Arguments

`f` | Nonexceedance probability (0 <= F <= 1).
`para` | The parameters from `parcau` or `vec2par`.

### Value

Quantile value for for nonexceedance probability F.

### Author(s)

W.H. Asquith

### References

Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational Statistics and Data Analysis, vol. 43, pp. 299–314.

Gilchirst, W.G., 2000, Statistical modeling with quantile functions: Chapman and Hall/CRC, Boca Raton, FL.

### See Also

`cdfcau`, `parcau`, `vec2par`

### Examples

      para <- c(12,12)
      quacau(.5,vec2par(para,type='cau'))

[Package lmomco version 0.92 Index]